He makes clear his belief that it is the whole nation’s “social responsibility” to put Servicemen and women at the “front and centre of our national life”.

In an unprecedented intervention, he states that with Britain at war in Afghanistan, the public has to give full and unequivocal support to troops and their families.

His demand comes a week after he returned from his first visit since taking office to Afghanistan, where the number of British troops killed since 2001 stands at 299.

He writes that the trip reinforced his appreciation of the bravery of the Armed Forces, and he hails charities such as Help for Heroes. Mr Cameron also praises public support for repatriation ceremonies at Wootton Bassett and military parades elsewhere.

He also signals that the Government will do more to help servicemen’s families — particularly in housing and health — and provide better treatment for veterans with mental health problems.

“These people know all about duty – they’ve lived it. Now we as a country must do our duty by them,” the Prime Minister writes.

Invoking the wartime spirit of previous generations, he adds: “There is huge respect for the Armed Forces out there, and I want that expressed more loudly and more proudly.”

The focus for such celebrations will be Armed Forces Day on Saturday. This annual event was started last year following a campaign by The Sunday Telegraph. The centrepiece of next weekend’s celebrations will be in Cardiff, including a parade led by the Prince of Wales, fly-pasts, a concert and a firework finale.

Mr Cameron writes: “Silent gratitude isn’t much use to anyone — so next Saturday I hope we see an explosion of red, white and blue all over the country.” Building on the theme of the “Big Society” — the Tory election platform that called for greater public involvement in state-provided services — he adds: “Supporting our Armed Forces isn’t just a government responsibility — it’s a social responsibility.”

Last week Mr Cameron won praise in Northern Ireland and elsewhere for his presentation of Lord Saville’s report into Bloody Sunday, which found that 14 people were killed by British soldiers without justification in Londonderry in January 1972.

On Tuesday Mr Cameron apologised for the actions of the soldiers, telling the Commons: “You do not defend the British Army by defending the indefensible.”

But today he seeks to move on, writing: “Those wrongs cannot be allowed to cloud the reputation of our Armed Forces and the pride they inspire.”

Mr Cameron signals that the forthcoming review of the military covenant, the contract between the forces and the Government, will do more to help military families, including obligations to provide decent levels of housing and measures to stop them being “pushed down” NHS waiting lists when they move bases.

He also promises better treatment for veterans, particularly “those who gave years of their life to mental illness, alcoholism or just a persistent feeling of alienation once they get home”.

Andrew Lansley, the Health Secretary, is trying to ensure the NHS and the Ministry of Defence work together to better co-ordinate services for ex-Servicemen with mental health problems.

Liam Fox, the Defence Secretary, has signalled that the Government was keen to “draw a line” under past failures in Afghanistan, including persistent complaints about equipment.

As part of this process Air Chief Marshal Sir Jock Stirrup will step down early as Chief of the Defence Staff. The most senior civil servant at the MoD, Sir Bill Jeffrey, will also go.